1. Field of Invention
This invention relates to designing zero-shift supercell halftone screens.
2. Description of Related Art
With the advent of inexpensive digital printers, methods and systems for digital halftoning have become increasingly important. It is well understood that most digital printers operate in a binary mode, i.e., printing or not printing a halftone dot at a specified location or pixel. Digital halftoning controls the printing of halftone dots, where spatially averaging of the printed dots provides the illusion of the continuous tones present in an original image.
The most common halftone technique is threshold screening, which compares the image value of each pixel in the original image with one of several predetermined threshold levels that are stored in a halftone screen. If the image value is “darker” than the applied threshold halftone level, a spot of ink or toner is printed at that pixel. Otherwise, the pixel is left unprinted, so that the background color of the image receiving medium is visible. It is well understood in the art that the distribution of printed pixels depends on the design of the halftone screen.
Halftone screens are typically two-dimensional threshold arrays and are relatively small in comparison to the overall image or document to be printed. Therefore, the screening process uses an identical halftone screen cell repeated for each color separation in a manner similar to tiling. The output of the screening process, using a single-cell halftone dot, includes a binary pattern of multiple small “dots”, which are regularly spaced and are determined by the size and the shape of the halftone screen. In other words, the screening output, as a two-dimensionally repeated pattern, possesses two fundamental spatial frequencies, which are completely defined by the geometry of the halftone screen.
It should be appreciated that, in the halftoning arts, square halftone cells, tiled in a zero-shift manner, can be easily combined to form a supercell. In contrast, non-zero-shift tiling results in a brick-like pattern, where the cells of one row are laterally offset relative to the upper and lower adjacent rows. Zero-shift refers to the corners of each of the square halftone supercells meeting at a common point. FIG. 1 illustrates two halftone supercells that have a non-zero shift. Because supercells are formed by combining a number of halftone cells, supercells can be used to form a “macro” halftone screen for halftoning the original image. Because a supercell is, by definition, larger than the individual halftone cells used to form the supercell, the resulting screen can have more threshold levels and can achieve better visual angles, on average, than the simple cell halftone. Reducing the number of centers in supercells that achieve the desired effects increases the efficiency of the supercell in conserving resources such as, for example, memory, processing power, and the like.
Conventionally, halftone screen designers have a number of conventional design tools usable to create a halftone screen utilizing supercells. In general, these conventional tools allow the halftone screen designer to create supercells based on magnifying Holladay dots. Holladay dots are described in “An Optimal Algorithm For Halftone Generation For Display And Hard Copies”, T. Holladay, Proceedings of the Society for Information Display, Vol. 21, No. 2, pages 185–192, 1980. As shown in FIG. 1, these conventional Holladay dots are described as a threshold array in an implementation rectangle that includes a shift between rows of tiled rectangles.
Current PostScript hafltoning implementations have difficulty using arbitrary Holladay dots. These software implementations of the PostScript standard are usually optimized for PostScript type 3 dots. In particular, PostScript type 3 dots are zero-shift-square tiles that abut at the corners, as outlined above. These software implementations of the PostScript standard also work most efficiently when these square tiles contain a multiple of 32 pixels per tile.